Simulating a plurality of fibers

ABSTRACT

A computer-implemented method for simulating a plurality of fibers is disclosed. It may be applied in particular for simulating the mechanical behavior of a tress or head of hair, woven or nonwoven fabrics, brushes, or other products incorporating fibrous material. The method comprises: providing a computational model for describing mechanical behavior of fibers; obtaining a set of fiber mechanical parameters, associated with fibers of a predetermined type, for use with the computational model; obtaining geometry information, describing the shape and position of the plurality of fibers to be simulated; and simulating, using the computational model, the set of fiber mechanical parameters, and the geometry information, a change in configuration of the plurality of fibers, to produce a second geometry information.

FIELD OF THE INVENTION

The present invention relates to a computer-implemented method forsimulating a plurality of fibers. The method may be applied inparticular for simulating the mechanical behavior of a tress or head ofhair. It can also be applied for simulating woven or nonwoven fabrics,brushes, or other products incorporating fibrous material.

BACKGROUND OF THE INVENTION

It is known to try to simulate an assembly of fibers, such as a tress orhead of hair, for example for computer graphics animation. However,known approaches are not realistic enough. In particular, they tend notto capture the mechanical behavior of the fibers in a physicallyaccurate way. It would be desirable to simulate fibers, such as hair, ina way that was more faithful to the mechanical behavior of those fibersin the real world.

SUMMARY OF THE INVENTION

The invention is defined by the claims.

According to an aspect of the invention, there is provided acomputer-implemented method for simulating a change in configuration ofa plurality of fibers, the method comprising:

providing a computational model for describing mechanical behavior offibers;

obtaining a first set of fiber mechanical parameters, associated withfibers of a predetermined type, for use with the computational model;

obtaining first geometry information, describing the shape and positionof the plurality of fibers to be simulated; and

simulating, using the computational model, the first set of fibermechanical parameters, and the first geometry information, the change inconfiguration of the plurality of fibers, to produce second geometryinformation,

wherein the first set of fiber mechanical parameters includes at leastone, any two, or all three of:

-   -   one or more coefficients of friction between fibers of the        predetermined type;    -   a measure of cohesion among fibers of the predetermined type;        and    -   a measure of adhesion among fibers of the predetermined type.

The present inventors have recognized that there is a need for bettercharacterization of the mechanical parameters of fibers in general andof hair fibers in particular. Whereas previous approaches have focusedon the stiffness or flexibility of individual fibers, the presentinventors have found that accurate characterization of the interactionsbetween fibers is important for the overall accuracy of a simulation ofa plurality of fibers. The behavior of a body made of fibers isinfluenced by the complex network of collisions (contact points) betweenthe fibers, and how the fibers interact when they collide. Friction,cohesion, and adhesion have been found to be the three most importantparameters governing interactions between fibers.

Adhesion refers to a force that opposes the separation of two hairfibers that are in contact with one another, where there is no liquidpresent at the point of contact.

Cohesion refers to a force that opposes the separation of two hairfibers that are in contact with one another, where there is a liquidpresent between them at the point of contact. Cohesion depends oncapillary forces and the Laplace pressure.

The cohesion and adhesion forces are preferably normalized by the areaof contact, in the set of fiber mechanical parameters.

Preferably, the first set of fiber mechanical parameters includes two ormore coefficients of friction, wherein each coefficient of frictionpertains to a different mutual orientation. This can allow anisotropicfriction effects to be described.

The first set of fiber mechanical parameters preferably further includesat least one, any two, or all three of: a Young's modulus associatedwith fibers of the predetermined type; a shear or torsional modulusassociated fibers of the predetermined type; and a bending modulusassociated with fibers of the predetermined type.

The parameters characterizing interactions between fibers are preferablycombined with an accurate characterization of the mechanicalcharacteristics of the individual fibers. In particular, it isadvantageous to characterize the flexibility of individual fibers insufficient detail. In this regard, the Young's modulus, the bendingmodulus and the torsional modulus have been found to be the mostimportant parameters. Torsional modulus is related to shear modulus.

The first set of fiber mechanical parameters preferably further includesat least one, any two, or all three of: a diameter associated withfibers of the predetermined type; a material density of fibers of thepredetermined type; and a cross-sectional shape or an ellipticityassociated with fibers of the predetermined type

It is advantageous to combine these other fiber mechanical parameterswith the parameters discussed above characterizing interactions andcharacterizing the flexibility of individual fibers.

The change in configuration that is simulated optionally comprises atleast one of: motion of the fibers; mechanical manipulation of thefibers; shortening or lengthening of the fibers; and a chemical orphysical treatment of the fibers that modifies their mechanicalbehavior.

In general, the change in configuration may be associated with a changein the geometry of the fibers, or a change in their mechanicalparameters, or both. Motion, mechanical manipulation (such as combing,braiding, or grooming), and cutting of the fibers may be associated withchanges in the geometry of the fibers. Chemical treatment such asshampooing, conditioning, coloring, perming, relaxing, or bleaching maybe associated with changes in the mechanical parameters. Heat treatmentsuch as crimping, curling, straightening, or blow-drying may beassociated with changes in both the geometry and the mechanicalparameters.

The method may further comprise: providing a database comprising a setof fiber mechanical parameters for each of a plurality of differenttypes of fiber, wherein the step of obtaining the first set of fibermechanical parameters comprises choosing one of the sets in thedatabase.

Different types of fiber may respond very differently to changes inconfiguration; therefore, it is desirable to be able to accuratelycharacterize the mechanical behavior of the particular type of fiberthat is to be simulated. Nevertheless, measuring fiber mechanicalparameters may be difficult, time-consuming, or in some casesimpossible, for given fibers in the real world. It may therefore beadvantageous to provide a database or library of fiber mechanicalparameters, which records the fiber mechanical parameters of types offibers that have previously been measured. The fiber mechanicalparameters for the simulation can then be retrieved from this database,for example, by selecting the type of fiber from a list.

Using a database or library like this can also allow simulation of theeffect of a change in the fiber parameters, by replacing one set offiber mechanical parameters chosen from the database with another set.

The database may comprise one or more additional sets of fibermechanical parameters for each type of fiber, wherein each of the one ormore additional sets characterizes the mechanical parameters of thattype of fiber after a respective chemical or physical treatment.

If the fibers are hair fibers, for example, this can allow prediction ofthe geometry (and therefore appearance) of a head of hair after a giventreatment is applied to it. The treatment will change the mechanicalparameters and the simulation predicts how this will alter theconfiguration (geometry) of the hair.

The first and second geometry information preferably describes thepositions of a plurality of segments of each of the fibers.

In this case, the computational model may model each fiber as a chain ofsegments.

The geometry information may also comprise a junction distribution amongfibers of the predetermined type. Alternatively, the junctiondistribution may be implicit in the geometry information and/or may bedetermined from it during the simulation. Together with the secondgeometry information (that is, the position of each segment), thesimulation optionally also outputs a velocity of each segment.

The first geometry information may be obtained from a real sample offibers and the step of obtaining the first geometry informationpreferably comprises at least one of: micro computed tomography; laserscanning; IR-imaging; and optical coherence tomography.

Obtaining geometry information from a real sample of fibers in this waycan allow more accurate capture of fiber geometry. It can also allowsimulation of a change in configuration of the real fibers in their realgeometry. Thus, it can allow a virtual prediction of a change inconfiguration of fibers in the real world.

The computational model may comprise at least one of: a Cosserat rod foreach fiber; a finite element based description for each fiber; aKirchoff rod for each fiber; and an oscillator network for each fiber.

Optionally, the oscillator network for each fiber may comprise acuboidal or tetrahedral oscillator network.

The computational model preferably also takes into account environmentalconditions, including but not limited to: temperature, humidity, andstochastic wind effects.

The method may further comprise rendering, based on the simulation, oneor more images showing the plurality of fibers after the change inconfiguration.

Rendering an image can allow the change in configuration to bevisualized. Rendering a plurality of images can allow the change inconfiguration to be visualized as an image sequence (for example, ananimation or movie).

The plurality of fibers preferably comprises a tress of hair or a headof hair.

When the fibers are hair fibers, the different types of fiber may beassociated with different hair colors, different ethnicities, and/ordifferent levels of damage. Preferably, sets of fiber mechanicalparameters for these different types of hair are stored in the database.

The method optionally further comprises: receiving target geometryinformation defining a desired configuration of the plurality of fibers;and deriving, based on the target geometry, a target set of fibermechanical parameters suitable for producing the target geometry,wherein deriving the target set of fiber mechanical parameterspreferably comprises: generating a plurality of modified sets of fibermechanical parameters; for each of the modified sets, simulating thechange in configuration produced by that modified set; and selecting asthe target set the modified set which produces a change in configurationthat best approximates the target geometry.

This uses an analysis-by-synthesis approach, preferably deriving thetarget set of fiber mechanical parameters by iterating the simulationsummarized earlier above.

Also provided is a non-transitory computer readable medium comprising acomputer program comprising computer program code configured to controla physical computing device to perform all the steps of a method assummarized above when said program is run on the physical computingdevice.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic block diagram illustrating an exemplary computersystem upon which embodiments of the invention may run;

FIG. 2 is a flow diagram showing a logical information flow in a methodaccording to an embodiment of the invention;

FIG. 3 is a flowchart of a simulation method according to an embodiment;

FIG. 4 is a flow diagram showing a logical information flow in a methodaccording to a further embodiment of the invention;

FIG. 5 is a flowchart of an inverse simulation method according to anembodiment; and

FIG. 6A is a schematic illustration of a way of measuring Young'smodulus for a single fiber; and

FIG. 6B is a schematic illustration of a fiber suspended between twosuspension points in order to measure bending modulus.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1 of the accompanying drawings schematically illustrates anexemplary computer system 100 upon which embodiments of the presentinvention may run. The exemplary computer system 100 comprises acomputer-readable storage medium 102, a memory 104, a processor 106 andone or more interfaces 108, which are all linked together over one ormore communication busses 110. The exemplary computer system 100 maytake the form of a conventional computer system, such as, for example, adesktop computer, a personal computer, a laptop, a tablet, a smartphone, a smart watch, a virtual reality headset, a server, a mainframecomputer, and so on.

The computer-readable storage medium 102 and/or the memory 104 may storeone or more computer programs (or software or code) and/or data. Thecomputer programs stored in the computer-readable storage medium 102 mayinclude an operating system for the processor 106 to execute in orderfor the computer system 100 to function. The computer programs stored inthe computer-readable storage medium 102 and/or the memory 104 mayinclude computer programs according to embodiments of the invention orcomputer programs that, when executed by the processor 106, cause theprocessor 106 to carry out a method according to an embodiment of theinvention

The processor 106 may be any data processing unit suitable for executingone or more computer readable program instructions, such as thosebelonging to computer programs stored in the computer-readable storagemedium 102 and/or the memory 104. As part of the execution of one ormore computer-readable program instructions, the processor 106 may storedata to and/or read data from the computer-readable storage medium 102and/or the memory 104. The processor 106 may comprise a single dataprocessing unit or multiple data processing units operating in parallelor in cooperation with each other. The processor 106 may, as part of theexecution of one or more computer readable program instructions, storedata to and/or read data from the computer-readable storage medium 102and/or the memory 104.

The one or more interfaces 108 may comprise a network interface enablingthe computer system 100 to communicate with other computer systemsacross a network. The network may be any kind of network suitable fortransmitting or communicating data from one computer system to another.For example, the network could comprise one or more of a local areanetwork, a wide area network, a metropolitan area network, the internet,a wireless communications network, and so on. The computer system 100may communicate with other computer systems over the network via anysuitable communication mechanism/protocol. The processor 106 maycommunicate with the network interface via the one or more communicationbusses 110 to cause the network interface to send data and/or commandsto another computer system over the network. Similarly, the one or morecommunication busses 110 enable the processor 106 to operate on dataand/or commands received by the computer system 100 via the networkinterface from other computer systems over the network.

The interface 108 may alternatively or additionally comprise a userinput interface and/or a user output interface. The user input interfacemay be arranged to receive input from a user, or operator, of the system100. The user may provide this input via one or more user input devices(not shown), such as a mouse (or other pointing device, track-ball orkeyboard. The user output interface may be arranged to provide agraphical/visual output to a user or operator of the system 100 on adisplay (or monitor or screen) (not shown). The processor 106 mayinstruct the user output interface to form an image/video signal whichcauses the display to show a desired graphical output. The display maybe touch-sensitive enabling the user to provide an input by touching orpressing the display.

According to embodiments of the invention, the interface 108 mayalternatively or additionally comprise an interface to a measurementsystem, for measuring fiber mechanical parameters of real fibers. Insome embodiments, the interface 108 may comprise an interface to ageometry capture system, such as a 3-D scanner, for capturing thegeometry of a plurality of real fibers.

It will be appreciated that the architecture of the computer system 100illustrated in FIG. 1 and described above is merely exemplary and thatsystems having different architectures using alternative components orusing more components (or fewer) may be used instead.

In the following, the invention will be described in the context ofembodiments in which the fibers are hair fibers. However, as will beapparent to those skilled in the art, the scope of the invention is notlimited to such embodiments and it can be used to simulate any type offiber.

FIG. 2 illustrates a logical information flow in a method according toan embodiment of the invention. A simulation 240 of a plurality offibers relies on three pieces of information: a computational model 210;a set of fiber mechanical parameters 220; and first geometry information230. The simulation 240 combines these to simulate a change inconfiguration of the plurality of fibers. The new configuration isrepresented by second geometry information 250.

The computational model 210 preferably models each fiber as a chain ofindividual segments. The first geometry information 230 provides theinitial positions for each of the segments of each fiber. The simulation240 steps incrementally forward in time, starting from these initialpositions (and optionally also information about initial velocities),using the computational model 210 to describe the mechanical behavior ofthe system of fibers. The mechanical response of the computational model210 is governed by the values of the fiber mechanical parameters 220.

In this embodiment, the fibers are hair fibers and the aim is tosimulate a change in configuration of a head of hair. The change ofconfiguration to be simulated may be a virtual representation of a real(that is, physically realizable) modification or manipulation of thehair. It may include motion of the hair, for example under gravity ordue to some perturbation, but simulation of motion is not essential.

FIG. 3 is a flowchart of a simulation method according to an embodiment.In step 310, the computational model 210 is provided. The computationalmodel 210 may be stored in the storage medium 102 from where it isretrieved by the processor 106. Next, in step 320, the processor 106obtains a first set of fiber mechanical parameters associated withfibers of a predetermined type, for use with the computational model210. In step 330, the processor 106 obtains first geometry information230 describing the shape and position of the plurality of fibers to besimulated. Then, in step 340, the processor 106 uses the computationalmodel 210, the fiber mechanical parameters 220, and the first geometryinformation 230 to simulate the change in configuration of the fibers.The output of the simulation is second geometry information, describingthe new shape and/or position of the fibers. Optionally, in step 350,the processor 106 renders one or more images of the fibers, based on thesecond geometry information produced by the simulation. This can allow auser to inspect the new hair geometry on a display screen.

In the embodiment pictured in FIG. 3, the first geometry information 230is obtained from a real sample of fibers. Specifically, the processor106 obtains the geometry information from Optical Coherence Tomography(OCT) apparatus 370. OCT apparatus 370 is interfaced to the computersystem 100 via interface 108. Optical coherence tomography can be usedto capture the 3-D geometry of a body of hair fibers as it is sensitiveto differences in the refractive index of materials. OCT can allowindividual structures to be resolved with high-resolution. The realsample of fibers used to generate the geometry information may be asmall tress of hair or a full head of hair.

In general, it may not be possible to obtain measurements of fibermechanical parameters 220 from the same sample of hair used to generatethe first geometry information 230. For example, measuring the fibermechanical parameters may require the hair to be cut, damaged, and/ortested in complex measurement equipment. To avoid the need to measurefiber mechanical parameters directly from the tress or head of hair thatwas used to generate the geometry information, in step 330 of FIG. 3 theprocessor 106 obtains the first fiber mechanical parameters from adatabase 360. This database stores fiber mechanical parameters for eachof a plurality of different hair types. These types may be definedaccording hair color (for example, blonde hair, red hair, dark hair)and/or ethnicity (for example, Afro-Caribbean hair, Western Europeanhair, etc.). The database preferably stores fiber mechanical parametersassociated with each of these hair types in each of a plurality ofstates of damage. And for each hair type at each level of damage, thedatabase preferably stores fiber mechanical parameters associated withthe results of a plurality of different hair treatments, as well as forthe “virgin” untreated hair. Thus, when indexed by specifying a hairtype, level of damage, and hair treatment, the database will return therelevant fiber mechanical parameters for use with the computationalmodel. This database can be constructed in advance, by mechanicalanalysis of suitable small samples of hair.

In the present embodiment, the set of fiber mechanical parameterscomprises a hair mechanical fingerprint including six parameters. Threeparameters define the interactions between hair fibers; these are: atleast one coefficient of friction between fibers; the cohesion amongfibers; and the adhesion among fibers. Three further parameters definethe mechanical characteristics of individual fibers; these are: theYoung's modulus of the fibers; the torsional modulus of the fibers; andthe bending modulus of the fibers. Preferably, the set of fibermechanical parameters also includes: the diameter of the fibers; theellipticity of the cross-sectional shape of the fibers; and the materialdensity of each fiber. The fiber mechanical parameters will be discussedin greater detail later below.

In the present embodiment, the computational model describing each fiberis based on a Cosserat rod, discretized into segments. The Cosserat rodmodel itself will be familiar to those skilled in the art. The modelalso includes a measure of damping in the hair fiber system, whichdescribes the interaction of the fibers with air or other gaseoussubstances and or water or other liquids. The damping effect is afunction of environmental conditions such as temperature and humidity;therefore, it is not part of the fiber mechanical parameters but rathera global parameter of the computational model.

As explained previously above, the geometry information defines thestarting position of each segment of each fiber in the model. Thesimulation determines the number of connection points between fibersbased on the geometry information. This is done usingcollision-detection functionality in the software. The number ofconnection points defines a junction distribution of the plurality offibers.

The simulation method illustrated in FIG. 3 can be used for a variety ofdifferent purposes.

In a first example, the simulation can be used to simulate a change inhairstyle. This can be done as part of a consultation with a customer ina hair salon. In this case, the first geometry information describes thestarting hairstyle. The first geometry information defines the positionof each hair fiber in a virtual head of hair. This virtual head of hairmay be based on the captured 3-D geometry of the customer's existinghairstyle. The fiber mechanical parameters for simulating the hair areobtained from the database 360. The database entry is chosen which bestmatches the ethnicity, hair color, and level of damage of the customer'sactual hair. To simulate cutting the hair, the length of each fiber inthe virtual head of hair may be shortened. The method then simulates theeffect of having changed the lengths of the fibers—stepping forward intime until the position of each hair reaches a steady state again. Thenew steady-state geometry of the hair fibers represents the result ofthe haircut for that customer. This can allow a physically accurateprediction of how the customer's hair will appear after cutting. Thisprediction can be rendered and displayed on a screen for the customer'sapproval or feedback.

If desired, the method can also simulate the effect of the hair growingback, after the haircut. This is done by successively increasing thelength of each fiber in the virtual head of hair and rerunning thesimulation at each length. This can allow an animated sequence of imagesto be rendered, showing how the cut hair will grow out over time.

As a further option, if desired, the method can also be used to simulatethe dynamic appearance of the new haircut. This can be done by(virtually) moving or shaking the position of the head in thesimulation. The simulation then steps forward incrementally in time, topredict how the hair fibers will follow the movement of the head. Imagesare rendered at each step, to create, frame-by-frame, an animation ofthe moving head of hair.

If the customer will be going on holiday to a different country, thesimulation can be programmed with the climatic and/or weather and/orwater conditions in that country. This can allow the appearance of thehairstyle to be predicted under those environmental conditions (whichmay be different from the conditions in the hair salon). For example, anincrease in humidity may make the hair heavier, may change itsstiffness, and/or may increase frizz; or a change in the mineral contentof the water used for hair cosmetic treatment can make the hair stifferor softer. These changes may suitably be simulated by the method.

As will be apparent from the foregoing, simulations such as these canallow a hairdresser or stylist to communicate with a customer moreeffectively. Customers may be reassured by the ability to predict thefinal outcome of the hair cutting and may be able to instruct thehairdresser/stylist more clearly as to their wishes.

In a second example, the method can be used to simulate the treatment ofa customer's hair with a hair cosmetic product. Again, this might bedone as part of a consultation with a customer in a hair salon.Alternatively, it could be done at a point-of-sale of the hair cosmeticproduct, such as in a retail store selling beauty products. To supportthis use-case, the database 360 includes fiber mechanical parameters fordifferent types of hair when treated by different hair cosmeticproducts. Note that these fiber mechanical parameters may be obtainedfrom small samples of the relevant types of hair in advance. This avoidsthe need to treat a whole head of hair with the hair cosmetic product.Nevertheless, using the method of FIG. 3, the appearance of a whole headof hair treated by the hair cosmetic product can be predicted by virtualsimulation. The first geometry information may be obtained by a 3-D scanof the customer's head. The customer (or a hair stylist or product salesassistant) then inputs the type of the customer's hair manually—forexample, by selecting the customer's ethnicity, hair color, and level ofdamage from drop-down menus in a user interface.

The method can then simulate the steady-state geometry of the customer'shair after treatment by the hair cosmetic product, by using thecorresponding stored set of hair fiber mechanical parameters from thedatabase 360. Essentially, the simulation allows extrapolation from atest on a small sample (tress) of hair to predict the appearance of afull head of hair.

An image showing the predicted appearance of the customer's hair aftertreatment can be rendered and displayed to the customer. Optionally, animage can also be rendered of the customer's hair in its currentgeometry. This can allow a side-by-side comparison of two virtualimages, showing the predicted difference in appearance as a result ofusing the hair cosmetic product.

Simulations such as this may also be useful in industrial researchlaboratories, for the development of new hair cosmetic products. Insteadof extensively testing the new product formulation on real models in atest salon, the method of FIG. 3 can be used to simulate the effect ofthe product on the appearance of many different heads of hair, withdifferent hairstyles. This can be achieved while only needing to treatsmall samples of hair (to determine hair fiber mechanical parameters forthe different hair types after treatment, in order to populate thedatabase 360). It may also be possible to interpolate among treatmentresults. For example, the new product formulation could be testedfirstly on blonde hair with a light level of damage, and secondly onblonde hair with a heavy level of damage, measuring the hair fibermechanical parameters from a small tress of treated hair in each case.The method may then interpolate the hair fiber mechanical parameters forblonde hair with a medium level of damage, by linear or nonlinearinterpolation between the hair fiber mechanical parameters for the twoextreme cases. In this way, the number of real experiments needed can bereduced, while obtaining a richer set of information about the likelyeffect of the new product formulation. This feedback can be used toguide the development process, helping product formulation experts toarrive at a suitable product formulation in a smaller number ofiterations and with a smaller number of tests than was previouslypossible.

Other virtual experiments with the hair fibers can also be conducted ina similar way. For example, the method can be used to simulateinteractions such as brushing or combing the hair.

Further details of the fiber mechanical parameters will now be provided.

There are several ways to measure friction, adhesion, and cohesion. Thiscan be done using an assembly of multiple fibers (wherein the number offibers is preferably known). Alternatively, it can be done by measuringinteractions between single fibers. For example, Atomic Force Microscopy(AFM) with modified tips can be used to measure the interactions betweenone single fiber and another single fiber. Conventionally, AFM uses acantilever with a sharp tip (such as a Silicon crystal) as a probe. Touse AFM with hair fibers, this sharp-tipped probe is replaced with ashort piece of hair fiber (<1 mm). The fiber may be mounted in a resin,in order to secure it. A second fiber is mounted on the AFM stage in asimilar manner. The interactions between the two fibers can then bemeasured by the AFM apparatus. Alternatively, the tip of theconventional probe can be chemically functionalized—for example with anamino functionalized (—NH3⁺) coating. This will cause a greaterattraction between the tip (which is now positively charged) andnegatively charged surface areas of the hair, characterized by —COO⁻—SO₃groups. This can be useful for detecting which parts of the hair fiberare uncoated and which parts are coated with a liquid. The applicationof AFM to hair fibers is described in Wood et al. (Claudia Wood, AlbertBudiman Sugiharto, Eva Max, and Andreas Fery, “From conditioning shampooto nanomechanics and haptics of human hair”, J. Cosmet. Sci., 62,259-264, March/April 2011). Friction, adhesion, and cohesion can also bemeasured using the so-called Surface Force Apparatus (SFA), furtherdetails of which can be found in Israelachvili et al. (J Israelachvili,Y Min, M Akbulut, A Alig, G Carver, W Greene, K Kristiansen, E Meyer, NPesika, K Rosenberg, and H Zeng, “Recent advances in the surface forcesapparatus (SFA) technique”, Reports on Progress in Physics, Vol. 73, No.3, 2010).

In the present embodiment, the preferred way of measuring the friction,adhesion and cohesion for use in the mechanical fingerprint is the SFA,as it can generate measurement conditions that are as close as possibleto the real world on the head of a person.

The coefficient of friction characterizes the amount of force requiredto move one hair fiber that is in contact with another hair fiber.Coefficients of friction are preferably measured for at least twodifferent mutual orientations of the motion vectors of the fibers,because hair fibers are not uniformly smooth and exhibit differentroughness and therefore a different coefficient of friction in differentdirections. Essentially, the measurement involves rubbing one fiberagainst the other and measuring the force required to do this. A similarmeasurement can alternatively be made with multiple fibers of the sametype rubbing against each other at the same time, by dividing by thenumber of fibers. In the present embodiment, the coefficient of frictionis measured between hair fibers at 90° to one another. The first fiberis then moved along the longitudinal direction of the second fiber. Thecoefficient of friction is measured in each direction (sliding the firstfiber along the second fiber in the root-to-tip direction of the secondfiber; and sliding the first fiber along the second fiber in thetip-to-root direction). This gives two coefficients of friction for theset of fiber mechanical parameters. These coefficients are typicallyvery different to one another: the cuticle angle provides aninterlocking mechanism, when the first fiber is sliding against theup-lifted orientation of the cuticle; but when the sliding is in thecuticle scale direction, the coefficient of friction is about 50% lower.

Like the coefficients of friction, adhesion and cohesion are preferablydetermined by making force measurements using load cells, with the hairfibers at right angles to one another. The hair fibers may beencapsulated in resin at each end, in order to hold them in place.Whereas the friction measurement requires one fiber to slide along theother, the adhesion and cohesion measurements are made at individualjunction locations (crossover points).

The adhesion characterizes the “stickiness” of the fibers due to theirsurface properties—that is, their tendency to adhere to one another.Thus, adhesion can be derived by measuring the amount of force requiredto separate two fibers. In adhesion, no material transfer from one fiberto the opposite fiber occurs.

The cohesion characterizes the bonding between fibers caused by thepresence of liquid between them. It is common for liquid deposits to bepresent on the hair fibers. For example, even on natural, untreatedhair, glands in the hair follicle produce sebum, which is deposited onthe hair fiber. Although shampoo removes sebum, other hair treatmentsreplace it with other liquid deposits. For example, conditioner maydeposit silicone on the hair fibers.

The liquid is typically unevenly deposited along the length of a hairfiber. Therefore, the attractive forces between the fibers may bedifferent, depending on where the fibers cross. Adhesion characterizesthe bonding between fibers at a junction where no liquid is present.Cohesion characterizes the bonding between fibers at a junction withliquid present. Therefore, including cohesion in the set of fibermechanical parameters characterizes the effect of liquid deposits on thefibers, as well as the fibers themselves. For example, cohesion mightcharacterize the binding of two hair fibers at a junction via a siliconedroplet that connects them there. Cohesion is defined by the capillaryforces between the two fibers, caused by the liquid silicone droplet.

Totally clean hair fibers can be considered to have no deposits on theirsurface. Their outermost layer in this “virgin” state is the so-called18-MEA or F-layer. When hair is damaged, the F-layer is partly or fullyremoved and thus the surface properties of hair change from hydrophobicto hydrophilic. This different surface energy also influences thedeposition of active compounds on the hair surface. On hair withdifferent surfaces energies, hair cosmetic actives will depositdifferently, leading to different capillary forces between fibers,caused by hair cosmetic actives, causing different cohesionforces/energies.

To measure cohesion, one must find a crossover point between the twofibers where liquid is present. To measure adhesion, one must find acrossover point where no liquid is present. In the present embodiment,this is done by maintaining the fibers at right angles and shifting thefibers relative to one another, to select different crossover points.The presence or absence of liquid can be detected by illuminating thejunction with white light and analyzing an interference patternproduced.

The primary measurement for each of adhesion and cohesion is the forcenecessary to separate the two fibers from contact. Each forcemeasurement is preferably normalized by the area of contact between thetwo fibers, before including the normalized result in the fibermechanical parameters.

There are also several ways to measure Young's modulus, bending modulus,and torsional modulus. FIG. 6A is a schematic illustration of a way ofmeasuring Young's modulus for a single fiber. The fiber is suspendedbetween two suspension points and is extended longitudinally untilbreakage occurs. The stress versus strain curve is recorded as the fiberis stretched. The elastic modulus (Young's modulus) is determined as theslope of the linear part of the stress-strain curve.

To measure bending modulus, a fiber is again suspended between twosuspension points, as shown in FIG. 6B. The fiber is then cut, to leaveone free end suspended from an upper suspension point. The cut end ofthe fiber is pressed down on a plate comprising a force sensor. Thebending force and the bending modulus can then be determined. For allsingle fiber modulus measurements (Young's modulus; shear/torsionalmodulus, bending modulus) the knowledge of the cross sectional area orellipticity or minor and major axis of the ellipsis of the fiber isneeded at the point of measurement to normalize the measured forces tothe cross-section of the fiber The bending method gives informationabout the softness (flexibility) of a fiber.

The force measurements for determining the bending modulus and Young'smodulus can be conducted using a Dia-Stron MTT600 or FBS900 tester. Notethat, since the fiber in the bending method is cut beforehand, and thefiber in the tensile test is stretched to breakage, different fibersfrom the same sample should be used for each of these tests. Forexample, torsion and bending can be measured on one fiber, with thetensile properties being measured on a second fiber. Alternatively,torsion and tensile properties can be measured on one fiber, with thebending modulus being measured on a second fiber.

The torsional behavior of hair fibers has been reported in theliterature by several authors. This can be determined using the torsionpendulum method. For this method, a formula for calculating the ShearModulus G′ has been published. See for example Robbins (C. R. Robbins,“Chemical and Physical Behavior of Human Hair”, Springer-Verlag, 2002,4^(th) Edition). The formula is reproduced in equation (1) below. Thisequation is based on Ip the Polar Moment of Inertia of the CrossSection.

$\begin{matrix}\begin{matrix}{{{Shear}\mspace{14mu}{Modulus}\mspace{14mu} G^{\prime}} = {4\;\pi^{2}*L*{M/T^{2}}*{Ip}}} \\{= {128\;\pi*L*{M/T^{2}}*d^{4}}}\end{matrix} & (1)\end{matrix}$L=Length of fiber, [m]M=Moment of Inertia of Pendulum [kg*m²]T=Period of Oscillation [s]Ip=Polar Moment of Inertia of Cross Section [m⁴]d=Fiber Diameter

Originally, Ip in equation (1) was based on a circular fiber crosssection (see equation (2) below). It can be adapted to take into accountan elliptical cross section for Ip (see equation (3) below).For Circular Cross Section Ip=πd ⁴/32  (2)For Elliptical Cross Section Ip=π(dmin³ *dmax+dmax³ *dmin)/64  (3)

It has been found that calculating the Shear Modulus G′ by theseequations often results in a large standard deviation. Without wishingto be bound by theory, it is believed that this is due to a dependencybetween shear modulus and ellipticity of the hair fiber cross-section.Ellipticity=dmin/dmax, where dmin is the minimum diameter of the hairfiber cross-section and dmax is the maximum diameter. That is, dmin anddmax are the dimensions along the minor and major axes, respectively, ofthe elliptical cross-section.

It is therefore proposed to replace Ip with the Torsional Moment ofInertia of Cross Section (I_(t)), for elliptical cross-sections.It=(π(dmin³ *dmax³))/(16*(dmin² +dmax²))  (4)

This has been found to reduce the standard deviation with respect toellipticity. Accordingly, the torsional modulus in the set of fibermechanical parameters is preferably defined as the Shear Modulus G′,calculated using the torsional moment of inertia of cross-section—thatis, using I_(t) in place of Ip in equation (1) above.

The length of each fiber tested as described above is preferably in therange 1 cm to 3 cm. In some embodiments, the parameters may be measuredseparately for each of a plurality of segments of each hair fiber, fromroot to tip. This would allow the variation in mechanical parametersalong the length of a hair fiber to be captured; thereby potentiallyproviding greater accuracy in the simulation.

Many variations are possible to the embodiment described above. Forexample, the 3-D fiber geometry information may be obtained in differentways. One alternative to OCT is laser scanning of the plurality offibers. The raw data from a laser scan is a point cloud which needs tobe processed to form a 3-D structure of fibers. An advantage of laserscanning is that it recognizes a 3-D shape with high precision. Laserscanning can be used on humans with suitable safety precautions. Anotheralternative to OCT is micro computed tomography (μ-CT). This is x-rayimaging in 3-D using techniques similar to hospital CT scans but on asmaller scale with increased resolution: μ-CT can have a voxel size ofabout 25 μm or less. It may be more suitable for small tresses of hair,since it is able to investigate only a limited volume. Also, since itrelies on irradiating the sample with x-rays, it may be better suited tosmall laboratory samples rather than in vivo scanning of human hair. Afurther difficulty of μ-CT is that it may be difficult to distinguishindividual fibers due to fusion.

Hair geometry could also be captured by a combination of techniques—forexample, a combination of laser scanning and OCT—to allow for complete3-D hair geometry to be captured via stitching.

It is not essential that the fiber geometry information is obtained byscanning a real sample. The geometry information may be synthetic—forexample, it may be a virtual hairstyle designed using a computergraphics tool, which does not necessarily have any analog in the realworld.

In the embodiment described above, the computational model of each fiberwas based on a discretized Cosserat rod. Again, this is not essential.Other computational models are known in the art.

As mentioned previously, the scope of the present invention is notlimited to simulation of hair fibers. The plurality of fibers to besimulated maybe fibers of any type. For example, they may be fibers in awoven or nonwoven textile, or fibers forming bristles of a brush. Thefibers need not be simulated in isolation—for example, the interactionof fibers with other solid objects, liquids, or gases may be simulated.In one embodiment, the fibers to be simulated comprise the bristles of atoothbrush and the simulation comprises simulating the interaction ofthe bristles with teeth, gums, or other oral-cavity tissue. The methodwould allow the interaction of individual fibers with the surface of theteeth to be predicted. This may improve understanding of the processesinvolved, for example with a view to designing better toothbrushes orevaluating different brushing techniques in a virtual simulation.

FIGS. 4-5 illustrate an extension of the simulation method of FIG. 3.Once again, this method will be explained in the context of simulatinghair fibers, but those skilled in the art will understand that the scopeis not limited in this way.

FIG. 4 is a schematic flow diagram showing the logical information flowaccording to one exemplary embodiment. The input to the method is targetgeometry information 235. This may represent, for example, a desiredhairstyle that a stylist wishes to achieve for a customer. This targetgeometry information 235 is used by an inverse simulation 410 to derivea target-set of fiber mechanical parameters 225. The target-set is a setof fiber mechanical parameters that—if achieved—would allow the desiredhairstyle (as defined by the target geometry information) to be created.

The target fiber mechanical parameters can help to guide the stylist inachieving the desired hairstyle. For example, the stylist might see fromthe target mechanical parameters that the hair needs to exhibit lowerfriction and greater bending stiffness, in order to achieve the targetgeometry. Based on his/her expert knowledge, the stylist can then chooseappropriate treatments that would bring the hair closer to the targetset of parameters, thereby making it easier for the stylist to achievethe target geometry.

The method will be described in greater detail with reference to FIG. 5.In step 530, the processor 106 receives the target geometry information235. The target geometry information 235 may be generated or obtained ina variety of ways. In one example, the customer's wishes would betransferred to a 3-D virtual hairstyle by the stylist, during aconsultation. This could be done by starting from a 3-D scan of thecustomer's existing hairstyle and modifying it using computer graphicstools, in real time, in response to feedback from the customer.Alternatively, the starting point could be one of a number of entirelysynthetic “standard” hairstyles, stored in the storage medium 102 of thecomputer 100. The customer could choose the standard hairstyle that ismost similar to his or her desired target and could then—in consultationwith the stylist—adapt the geometry of this hairstyle to customize it tohis or her wishes. In another example, the target hairstyle could beextrapolated from a 2-D sketch or photo, to derive 3-D target geometryinformation. In each case, the target geometry information defines the3-D position of each segment of each hair fiber. In the presentembodiment, it is assumed that the velocity of each segment is zero—inother words, that the hair is motionless in the specified targetgeometry.

The inverse simulation 410 proceeds using an “analysis by synthesis”approach. This is initialized by choosing an initial set of fibermechanical parameters and adopting a starting geometry. The initial setof fiber mechanical parameters may be chosen randomly or may bedependent to some extent upon the target geometry information. Thestarting geometry may be based on the customer's current hairstyle. Theprocess then applies an iterative approach. In step 340, the processor106 simulates the configuration change that is caused by applying theinitial set of fiber mechanical parameters to the initial geometry. Theoutput of the simulation is geometry information describing theresulting geometry. In step 510, the processor compares this resultinggeometry with the target geometry. Assuming that the two are not yetsufficiently similar, the method proceeds to step 520. In this step, theprocessor 106 modifies the set of fiber mechanical parameters. Themethod then returns to step 340 again, for the processor to simulate thechange in configuration resulting from the application of the modifiedfiber mechanical parameters to the starting geometry. Again, the methodproceeds to step 510, to check if the new resulting geometry informationmatches the target geometry sufficiently well. At each iteration, thefiber mechanical parameters are modified so as to drive the resultinggeometry information towards the target geometry. This can be achievedin a number of ways, using a number of possible strategies to adjust theparameters. Such strategies include but are not limited to: gradientdescent methods; Monte Carlo methods; and genetic algorithms.

When the method determines, in step 510, that the current resultinggeometry information is sufficiently similar to the target geometry, theiterations terminate. At that point, the modified fiber mechanicalparameters from the final iteration are chosen as the target fibermechanical parameters (step 550). The iterations can be terminated basedon several possible rules. For example, the iterations may continueuntil the sum of squared differences between the current geometryinformation and the target geometry information is less than apredefined threshold. Alternatively, the iterations may continue untilthe sum of squared differences ceases to reduce between iterations.Those skilled in the art will appreciate that the sum of squareddifferences is merely one of a number of possible suitable metrics touse for assessing the quality of the geometry.

In the example of FIG. 5, the inverse simulation 410 was conducted byiterating the forward simulation and updating the fiber mechanicalparameters in each iteration. However, in general, it is not necessaryto follow an iterative approach. For example, a plurality of simulations340 could be run in parallel, using different fiber mechanicalparameters. This could be combined with an iterative approach, byiterating each of the parallel simulations, in a similar manner to thatdescribed above. This may allow faster and/or broader exploration of thefull parameter space.

It should be noted that the above-mentioned embodiments illustraterather than limit the invention, and that those skilled in the art willbe able to design many alternative embodiments without departing fromthe scope of the appended claims. In the claims, any reference signsplaced between parentheses shall not be construed as limiting the claim.The word “comprising” does not exclude the presence of elements or stepsother than those listed in a claim. The word “a” or “an” preceding anelement does not exclude the presence of a plurality of such elements.The embodiments may be implemented by means of hardware comprisingseveral distinct elements. In the device claim enumerating severalmeans, several of these means may be embodied by one and the same itemof hardware. The mere fact that certain measures are recited in mutuallydifferent dependent claims does not indicate that a combination of thesemeasures cannot be used to advantage. Furthermore, in the appendedclaims lists comprising “at least one of: A; B; and C” should beinterpreted as (A and/or B) and/or C.

Furthermore, in general, the various embodiments may be implemented inhardware or special purpose circuits, software, logic or any combinationthereof. For example, some aspects may be implemented in hardware, whileother aspects may be implemented in firmware or software which may beexecuted by a controller, microprocessor or other computing device,although these are not limiting examples. While various aspectsdescribed herein may be illustrated and described as block diagrams,flow charts, or using some other pictorial representation, it is wellunderstood that these blocks, apparatus, systems, techniques or methodsdescribed herein may be implemented in, as non-limiting examples,hardware, software, firmware, special purpose circuits or logic, generalpurpose hardware or controller or other computing devices, or somecombination thereof.

The embodiments described herein may be implemented by computer softwareexecutable by a data processor of the apparatus, such as in theprocessor entity, or by hardware, or by a combination of software andhardware. Further in this regard it should be noted that any blocks ofthe logic flow as in the Figures may represent program steps, orinterconnected logic circuits, blocks and functions, or a combination ofprogram steps and logic circuits, blocks and functions. The software maybe stored on such physical media as memory chips, or memory blocksimplemented within the processor, magnetic media such as hard disk orfloppy disks, and optical media such as for example DVD and the datavariants thereof, CD.

The memory may be of any type suitable to the local technicalenvironment and may be implemented using any suitable data storagetechnology, such as semiconductor-based memory devices, magnetic memorydevices and systems, optical memory devices and systems, fixed memoryand removable memory. The data processors may be of any type suitable tothe local technical environment, and may include one or more of generalpurpose computers, special purpose computers, microprocessors, digitalsignal processors (DSPs), application specific integrated circuits(ASIC), gate level circuits and processors based on multi-core processorarchitecture, as non-limiting examples.

Embodiments as discussed herein may be practiced in various componentssuch as integrated circuit modules. The design of integrated circuits isby and large a highly automated process. Complex and powerful softwaretools are available for converting a logic level design into asemiconductor circuit design ready to be etched and formed on asemiconductor substrate.

The dimensions and values disclosed herein are not to be understood asbeing strictly limited to the exact numerical values recited. Instead,unless otherwise specified, each such dimension is intended to mean boththe recited value and a functionally equivalent range surrounding thatvalue. For example, a dimension disclosed as “40 mm” is intended to mean“about 40 mm”.

All documents cited in the Detailed Description of the Invention are, inrelevant part, incorporated herein by reference; the citation of anydocument is not to be construed as an admission that it is prior artwith respect to the present invention. To the extent that any meaning ordefinition of a term in this written document conflicts with any meaningor definition of the term in a document incorporated by reference, themeaning or definition assigned to the term in this written documentshall govern.

While particular embodiments of the present invention have beenillustrated and described, it would be obvious to those skilled in theart that various other changes and modifications can be made withoutdeparting from the spirit and scope of the invention. It is thereforeintended to cover in the appended claims all such changes andmodifications that are within the scope of this invention.

What is claimed is:
 1. A computer-implemented method for simulating achange in configuration of a plurality of fibers, the method comprising:providing a computational model for describing mechanical behavior offibers; obtaining a first set of fiber mechanical parameters, associatedwith fibers of a predetermined type, for use with the computationalmodel; obtaining first geometry information, describing the shape andposition of the plurality of fibers to be simulated; and simulating,using the computational model, the first set of fiber mechanicalparameters, and the first geometry information, the change inconfiguration of the plurality of fibers, to produce second geometryinformation, rendering, based on the simulation, one or more imagesshowing the plurality of fibers after the change in configuration;wherein the first set of fiber mechanical parameters comprises: ameasure of cohesion among fibers of the predetermined type; a measure ofadhesion among fibers of the predetermined type; a shear modulusassociated fibers of the predetermined type; wherein the shear modulusis calculated using the Torsional Moment of Inertia of Cross-Section(I₁).
 2. The method of claim 1, wherein the first set of fibermechanical parameters is selected from the group consisting of: aYoung's modulus associated with fibers of the predetermined type; abending modulus associated with fibers of the predetermined type; andcombinations thereof.
 3. The method of claim 1, wherein the first set offiber mechanical parameters is selected from the group consisting of adiameter associated with fibers of the predetermined type; a materialdensity of fibers of the predetermined type; a cross-sectional shape oran ellipticity associated with fibers of the predetermined type; andcombinations thereof.
 4. The method of claim 1, wherein the change inconfiguration that is simulated is selected from the group consisting ofmotion of the fibers; mechanical manipulation of the fibers; shorteningor lengthening of the fibers; a chemical or physical treatment of thefibers that modifies their mechanical behavior; and combinationsthereof.
 5. The method of claim 1, further comprising: providing adatabase comprising a set of fiber mechanical parameters for each of aplurality of different types of fiber, wherein the step of obtaining thefirst set of fiber mechanical parameters comprises choosing one of thesets in the database.
 6. The method of claim 5, wherein the databasecomprises one or more additional sets of fiber mechanical parameters foreach type of fiber, wherein each of the one or more additional setscharacterizes the mechanical parameters of that type of fiber after arespective chemical or physical treatment.
 7. The method of claim 1,wherein the first and second geometry information describes thepositions of a plurality of segments of each of the fibers.
 8. Themethod of claim 1, wherein the first geometry information is obtainedfrom a real sample of fibers and the step of obtaining the firstgeometry information selected from the group consisting of microcomputed tomography; laser scanning; IR-imaging; and optical coherencetomography.
 9. The method of claim 1, wherein the computational model isselected from the group consisting of: a Cosserat rod for each fiber; afinite element based description for each fiber; a Kirchoff rod for eachfiber; an oscillator network for each fiber; and combinations thereof.10. The method of claim 1, wherein the plurality of fibers comprises atress of hair or a head of hair.
 11. The method of claim 1, furthercomprising: receiving target geometry information defining a desiredconfiguration of the plurality of fibers; and deriving, based on thetarget geometry, a target set of fiber mechanical parameters suitablefor producing the target geometry, wherein deriving the target set offiber mechanical parameters comprises: generating a plurality ofmodified sets of fiber mechanical parameters; for each of the modifiedsets, simulating the change in configuration produced by that modifiedset; and selecting as the target set the modified set which produces achange in configuration that best approximates the target geometry. 12.The method of claim 1, wherein the first set of fiber mechanicalparameters further comprises two or more coefficients of friction,wherein each coefficient of friction pertains to a different mutualorientation, thereby allowing anisotropic friction effects to bedescribed.
 13. A non-transitory computer readable medium comprising acomputer program comprising computer program code configured to controla physical computing device to perform all the steps of a methodaccording to any one of the preceding claims when said program is run onthe physical computing device.
 14. A computer-implemented method forsimulating a change in configuration of a plurality of fibers, themethod comprising: providing a computational model for describingmechanical behavior of fibers; obtaining a first set of fiber mechanicalparameters, associated with fibers of a predetermined type, for use withthe computational model; obtaining first geometry information,describing the shape and position of the plurality of fibers to besimulated; and simulating, using the computational model, the first setof fiber mechanical parameters, and the first geometry information, thechange in configuration of the plurality of fibers, to produce secondgeometry information, rendering, based on the simulation, one or moreimages showing the plurality of fibers after the change inconfiguration; wherein the first set of fiber mechanical parameterscomprises: a measure of cohesion among fibers of the predetermined type;a measure of adhesion among fibers of the predetermined type; a Young'smodulus associated with fibers of the predetermined type; a shearmodulus associated fibers of the predetermined type; a bending modulusassociated with fibers of the predetermined type.
 15. The method ofclaim 14, wherein the first set of fiber mechanical parameters furthercomprises: a diameter associated with fibers of the predetermined type;a material density of fibers of the predetermined type; and across-sectional shape or an ellipticity associated with fibers of thepredetermined type.